Monte Carlo study of three-dimensional—to—one-dimensional crossover in the Ising model

Monte Carlo calculations have been used to study the behavior of a simple cubic spin-{} Ising model with spatially anisotropic nearest-neighbor coupling. The interaction in the x and y directions, which is equal to (J_⊥), was systematically decreased compared to that in the z direction (J_∥), and results were obtained for values of Δ=J_⊥J_∥ as small as 0.003. For small Δ the system behaves like a one-dimensional Ising chain at high temperature before undergoing a low-temperature transition to a three-dimensionally ordered state. We find that the asymptotic (Δ→0) variation of Tc is accurate over a surprisingly wide range of Δ.